Peter K. Friz Martin Hairer With an Introduction to Regularity Structures Second Edition
Page 1 Universitext Peter K. Friz Martin Hairer A Course on Rough Paths With an …

In this paper, we explore the version of Hairer's regularity structures based on a greedier
index set than trees, as introduced in (Otto et al. in A priori bounds for quasi-linear SPDEs in …

We obtain a generalisation of the Stroock–Varadhan support theorem for a large class of
systems of subcritical singular stochastic partial differential equations driven by a noise that …

Malliavin calculus provides a characterization of the centered model in regularity structures
that is stable under removing the small-scale cut-off. In conjunction with a spectral gap …

The reconstruction theorem tackles the problem of building a global distribution, on ℝ d or
on a manifold, for a given family of sufficiently coherent local approximations. This theorem …

We implement a Laplace method for the renormalised solution to the generalised 2D
Parabolic Anderson Model (gPAM) driven by a small spatial white noise. Our work rests …

We study Malliavin differentiability of solutions to sub-critical singular parabolic stochastic
partial differential equations (SPDEs) and we prove the existence of densities for a class of …

Abstract (EN) This thesis is concerned with a solution theory for quasilinear singular
stochastic partial differential equations. We approach the theory of regularity structures, a …

In this thesis, we derive analytic results related to the theories of Rough Paths and
Regularity Structures, with the point of view of germs, that is, families of local approximations …

Absolute Continuity of Singular SPDEs and Bayesian Inference on Dynamical Systems Page 1
Absolute Continuity of Singular SPDEs and Bayesian Inference on Dynamical Systems by …